As discussed in Section REF  and further elaborated in Section REF , a significant population of dust-attenuated and -obscured galaxies has been suggested even at \(z>4\). As pointed out in [1]}, an accurate assessment of the total SFR (i.e., \({\rm SFR_{UV}}+{\rm SFR_{FIR}}\) ) and a robust inclusion of limits in C\(^+\)  and far-IR continuum is therefore crucial for such an analysis.
The total SFR of the ALPINE main targets are derived in [1]} as follows.
First, the dust uncorrected UV SFRs (\({\rm SFR_{UV}}\) ) are based on the rest-frame \(L_{\rm 1500}\)  luminosity derived from SED fitting at \(1500\,{\rm \text{\normalfont Å}}\)  (see details in [3]}) and by applying the [4]} relation, \({\rm SFR_{UV}} [{\rm M_{\odot }\,yr^{-1}}]~=~1.59 \times 10^{-10}\,L_{\rm 1500}/{\rm L_{\odot }}\)  converted to a [5]} IMF.
For the calculation of the infrared SFR (\({\rm SFR_{FIR}}\) ), the conversion from ALMA-measured single-point photometry at rest-frame \(\sim \)\(150\,{\rm m}\)  to total far-IR luminosity (\(L_{\rm IR}\) ) is crucial. The conversion depends strongly on the assumed shape of the far-IR SED (itself depending on many parameters including the warm and cold dust temperature), which is unknown as only one far-IR data point exists for the ALPINE galaxies. To compute the conversion factor, an average empirical far-IR template is created using the same approach as outlined in Section REF  (for details, see [6]}).
The far-IR SFRs for far-IR-continuum-detected galaxies are derived via \({\rm SFR_{FIR}} [{\rm M_{\odot }\,yr^{-1}}] = 1.40 \times 10^{-10}\,L_{\rm IR}/{\rm L_{\odot }}\)  [4]}, where the far-IR luminosity is again obtained by integration of the far-IR SED at 8–1000 \({\rm {m}}\) . For galaxies not detected in far-IR continuum (i.e., ALMA sub-mm), \(L_{\rm IR}\)  is derived from the stacked IRX\(-\beta \)  relationThe IRX\(-\beta \)  relation relates the rest-UV continuum slope (\(\beta \) , described in [3]}) to the \(L_{\rm IR}/L_{\rm UV}\)  (IRX) luminosity ratio. presented in [9]} (see also Section REF ).
